In the figure above, what are the coordinates of point R ?

Question

https://gmatclub.com/forum/download/file.php?id=41795 In the figure above, what are the coordinates of point R ? A. (3,−5) B. (3,−3) C. (5,5) D. (5,−3) E. (5,−5) (PS02599) xy.jpg

dcummins · Accepted Answer

https://i.imgur.com/MDlR1TK.jpg

I used the angle and length measurement to solve this. See my diagram below - I found this easiest.

ScottTargetTestPrep · Answer

Since the length of PQ is 5, the base of the triangle is 5. Since we have a 45-45-90 right triangle, the height is also 5. Since R has the same x-coordinate as Q, the coordinates of R are (5,-5).

Answer: E

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=tN8HGUFNymA

Heisenberg12 · Answer

We know that -

The line through point Q (5,3) is a vertical line with undefined slope. Thus, the x co-ordinate of the point R is 5.

Given that line through origin and point R is inclined 45 degree with the x-axis and it goes from left to right (bottom to top) - thus the slope is -1. Therefore, only if y co-ordinate is -5 will the slope of line OR be -1.

Thus, answer E.

Iakovos1995 · Answer

The x-coordinate of R is positive and the y-coordinate of R is negative. So answer C is out.
The x-coordinate of R is the same with the x-coordinate of Q which is 5. So answer A and B are out.
The triangle of the 4th quartile has angles in the ratio 45:45:90 since there is a right angle at the point where the QR intersects the x-axis. So the ratio of the sides of the triangle is x:x:sqrt2*x. The x equals 5 since equals with the side PQ. But R is in the 4th quartile so we need the negative value which is -5. The coordinates of R are (5,-5)
The correct answer is E.

master315 · Answer

Dimensions of the rectangle would be height = 3 , width = 5

We know that it's a right angle triangle 90 - 45 (given) = 45 (the unknown angle)

So since we know that lets now operate on the following sine rule :

Sine A (angle) / a (opp side length) = Sine B (angle) / b (opp side length)

Applying the above rule :

Sine 45 / 5 = Sine 45 / x 
(where x is the height of right angle triangle)

After computing we get x = 5.

Now the easiest part we know that right angle triangle is on negative side of Y Axis so it's -5 and we already know X Axis which is 5.

Therefore answer is 5,-5.

royharmon4 · Answer

Since the triangle has two 45 degree angles, is that enough to let you know that the base and height will be the same (i.e., R's x-value will be the same as Q)?

master315 · Answer

Yes, it's enough to let us know the height since only base length is known we compute it with that.

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle.

You can use the Law of Sines if you already know

> One side and its opposite angle, and
> One or more other sides or angles

Posted from my mobile device

Princ · Answer

OA: E
Equation of QR ,  x=5 
Equation of OR ,  y=-x 
The intersection point of Line QR and OR is R
Solving equation
 x =5  and  y=-x  , we get  x=5  and  y =-5 
Coordinate of R  : (5,-5)

gupta335 · Answer

We know that sides in a 90-45-45 angle are in the ratio root 2:1:1. Notice the triangle is 90-45-45

From point Q(5,3) we know that the length of base of the triangle is 5. Hence the height will also be 5, while the hypotenuse will be 5root2.

Therefore, the x coordinate will be 5(base) and y coordinate will be -5( Height)

Ans- E

KanishkM · Answer

IMO, no calculation was required, since in a PS question, the figures are drawn to scale.

Its even discussed here,https://gmatclub.com/forum/figures-drawn-to-scale-general-quant-question-279658.html

Only valid options were D and E.

Out of which only E wins, since the figure above the x axis will be a rectangle of area 15, which when inverted will make the same area.

BrentGMATPrepNow · Answer

One of my students asked for a more detailed solution. So, . . .

The coordinates of point Q give us information about the following lengths:
 https://i.imgur.com/DnirHW9.png

Now focus on the RIGHT triangle below:
 https://i.imgur.com/N5KACz2.png 
We can see the missing angle is 45°, which makes this an ISOSCELES right triangle.

Since we have an ISOSCELES right triangle, we know the length of the other leg is 5 
 https://i.imgur.com/53pgo2m.png

At this point, we have enough information to determine that point R has coordinates (  5  ,   -5  )
 https://i.imgur.com/mhIQI5g.png

Answer: E

Cheers,
Brent

shaonkarim · Answer

Since 45:45:90. I mean two sides are equal, where one side is given 5